I don't follow this line of argument. Theoretically the concern is exhaled droplets which I assume primarily come from your mouth. If the point of a mask is to protect others and not yourself then why would the nose need to be covered?
Even if that isn’t the case, your nose and mouth are connected, and both contain mucosal membranes. They’re sharing the same droplets.
In general, when you cough, sneeze, or even breathe, the same droplets are coming out of both your mouth and nose.